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Question

Derive expression for displacement, amplitude, velocity and acceleration. and show that phase difference between displacement and velocity is pi/2

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Solution

Displacement in SHM is given by x = A sin( wt) where A is amplitude, w is angular velocity, t is instantaneous time.

Velocity is rate of change of displacement with time. Differentiating displacement with respect to time, we have,

V = Aw cos(wt)

Phase difference between sin and cos function is 90 degrees or pi/2 radians . Hence phase difference between displacement and velocity is 90 degrees or pi/2 radians.

Similarly, acceleration can be obtained by differentiating equation of velocity.

Acceleration a = - Aw^2 sin (wt)

Hence phase difference between velocity and acceleration is also pi/2.

Phase difference between displacement and acceleration is pi radians or 180 degrees.

Hope this will clear concept.


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